The Porous Shallow water Equations are widely used in the context of urban flooding simulation. In these equations, the solid obstacles are implicitly taken into account by averaging the classic Shallow water Equations on a control volume containing the fluid phase and the obstacles. Numerical models for the approximate solution of these equations are usually based on the approximate calculation of the Riemann fluxes at the interface between cells. In the present paper, it is presented the exact solution of the one-dimensional Riemann problem over the dry bed, and it is shown that the solution always exists, but there are initial conditions for which it is not unique. The non-uniqueness of the Riemann problem solution opens interesting questions about which is the physically congruent wave configuration in the case of solution multiplicity.

Multiple Solutions for the Riemann Problem in the Porous Shallow Water Equations / Cozzolino, Luca; Castaldo, Raffaele; Cimorelli, Luigi; Della Morte, Renata; Pepe, Veronica; Varra, Giada; Covelli, Carmine; Pianese, Domenico. - 3:(2018), pp. 476-484. (Intervento presentato al convegno HIC 2018. 13th International Conference on Hydroinformatics tenutosi a Enna nel 1-6 luglio 2018) [10.29007/31n4].

### Multiple Solutions for the Riemann Problem in the Porous Shallow Water Equations

#### Abstract

The Porous Shallow water Equations are widely used in the context of urban flooding simulation. In these equations, the solid obstacles are implicitly taken into account by averaging the classic Shallow water Equations on a control volume containing the fluid phase and the obstacles. Numerical models for the approximate solution of these equations are usually based on the approximate calculation of the Riemann fluxes at the interface between cells. In the present paper, it is presented the exact solution of the one-dimensional Riemann problem over the dry bed, and it is shown that the solution always exists, but there are initial conditions for which it is not unique. The non-uniqueness of the Riemann problem solution opens interesting questions about which is the physically congruent wave configuration in the case of solution multiplicity.
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2018
Multiple Solutions for the Riemann Problem in the Porous Shallow Water Equations / Cozzolino, Luca; Castaldo, Raffaele; Cimorelli, Luigi; Della Morte, Renata; Pepe, Veronica; Varra, Giada; Covelli, Carmine; Pianese, Domenico. - 3:(2018), pp. 476-484. (Intervento presentato al convegno HIC 2018. 13th International Conference on Hydroinformatics tenutosi a Enna nel 1-6 luglio 2018) [10.29007/31n4].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11588/723105`
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